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In accordance with the Bohr's model, fin...

In accordance with the Bohr's model, find the quantum number that characterizes the earth's revolution around the sun in an orbit of radius `1.5xx10^(11)m` with orbital speed `3xx10^4m//s`. (Mass of earth=`6.0xx10^(24)kg`)

Text Solution

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Given , radius of orbit `r=1.5xx10(^(11)m`
orbital speed `v=3xx10^(4)m//s` ,
Mass of earth `M=6xx10^(24)kg`
Angular momentum, `mvr=(nh)2pi` or `n=(2pivrm)/h` [ where,n is the quantum number of the orbit]
` (2xx3.14xx3xx10^(4)xx1.5xx10^(11)xx6xx10^(24))/(6.63xx10^(-34)`
` 2.57xx10^(74)` or `n=2.6xx10^(74)` which is too. thus. the quantum number is `2.6xx10^(74)` which is too large .
the electron would jump from `n=1`to `n=3`
`E_(3)=-13.6/3^(2)=-1.5eV`.
so, they belong to Lyman series.
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